Challenging questions are raised by the measurement of genomic and transcriptional aberrations in cancer cells. In a broad sense, answering these questions will further our understanding of cancer biology, guide more sensitive diagnosis, and ultimately improve therapy. These questions present clear opportunities for the development of statistical methods, since many sources of variation affect the measurements, and these need to be properly accommodated so that relevant biological signals can be detected. The four specific aims of the proposed project react to the demand for better statistical methods to study dependencies in multivariate profiles of genomic aberration and to study patterns of differential gene expression. Motivated by recent innovations in the stochastic modeling of genomic aberrations, the first three specific aims will extend and fully evaluate the model-based instability-selection approach to data analysis. The fourth aim focuses on new methodology to characterize patterns of differential gene expression among multiple groups. The proposed research merges advanced stochastic modeling techniques and tools from statistical computing to provide useful statistical methods for oncologists who study cancer at the molecular level.